 # Mathematics -I (65911/5911)

Subject Teacher : Md. Abdul Hakim, Sr. Assistant Director
Technology : Civil,Computer, Electrical, AIDT, Telecommunication, Textile & GDPM
Semester : 1st Semester

Subject Aims:
• To acquaint the students with the basic terminology of Algebra.
• To be able to understand the complex numbers which are being used in electrical engineering.
• To be able to understand the binomial expansion.
• To be able to use the knowledge of trigonometry in solving problems of engineering importance.

Subject Outcome:
Students will able to learn about Algebra and Trigonometry by studying this subject.
• Detail discussions in Algebra will be: AP & GP, Polynomials & polynomial equations, Complex number, Permutation & Combination, Binomial Theorem for positive integral index and negative & fractional index.
• Detail discussions in Trigonometry will be: Ratio of associated angles, Compound angles, Transformation formulae, multiple angles and Sub-multiple angles.

Private Course

Last Update 07/24/2020 6 hours 29 minutes 1
• Lecture 1 ( Chapter : Partial Fractions ) Define proper and improper fractions
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• Lecture 2 ( Chapter : Partial Fractions ) 1. Resolve in to partial fraction of the followings types : a) Denominator having a non-repeated linear factor. b) Denominator having a repeated linear factor c) Denominator having a quadratic factors. d) Denominator having a combination of repeated, non-repeated and quadratic factors.
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• Lecture 3 ( Chapter : Partial Fractions ) Solve problems related to combination.
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• Lecture 4 ( Chapter : The binomial theorem for positive index ) 1. State binomial expression. 2. Express the binomial theorem for positive index.
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• Lecture 5 ( Chapter : The binomial theorem for positive index ) Find the general term, middle term, equidistant term and term independent of x.
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• Lecture 6 ( Chapter : The binomial theorem for positive index ) Solve the problems related to the above.
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• Lecture 7 ( Chapter : The binomial theorem for positive index ) Solve the problems related to the above.
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• Lecture 8 ( Chapter : Binomial theorem for negative and fractional index ) Express the binomial theorem for negative and fractional index.
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• Lecture 9 ( Chapter : Binomial theorem for negative and fractional index ) Solve the problems related to the above.
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• Lecture 10 ( Chapter : Binomial theorem for negative and fractional index ) Solve the problems related to the above.
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• Lecture 12 ( Chapter : Complex numbers. ) 1. Find the cube roots of unity. 2. Apply the properties of cube root of unity in solving problems
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• Lecture 13 ( Chapter : permutation. )1. Explain permutation. 2. Find the number of permutation of n things taken r at a time when, i ) Things are all different. ii) Things are not all different.
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• Lecture 14 ( Chapter : permutation. ) Solve problems of the related to permutation :
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• Lecture 15 ( Chapter : Combination ) 1. Explain combination. 2. Find the number of combination of n different things taken r at a time
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• Lecture 16 ( Chapter : Combination ) 1. Explain nCr, nCn, nC0 2. Find the number of combination of n things taken r at a time in which p particular things i) Always occur ii) never occur Establish i) nCr = nCn-r ii) nCr + nCr-1 = n+1Cr
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• Lecture 17 ( Chapter : Combination ) Solve problems related to combination.
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• Lecture 18 ( Chapter : Set ) 1. Define set, sub-set and universal set. 2. Define the different types of number set.
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• Lecture 19 (Chapter : Set ) 3. Define union of set, intersection of set, complement of set, power set, disjoint set. 4. Prove (using Venn diagram) the relation of following types where A, B and C are any set.
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• Lecture 20 ( Chapter : Set ) 4. Find the number of elements in the union of two sets. 5. Solve the problems using above.
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• Lecture 21 (Chapter : Trigonometrical ratios and associated angles.) 1. Define associated angles. 2. Find the sign of trigonometrical function in different quadrants.
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• Lecture 22 ( Chapter : Trigonometrical ratios and associated angles ) 1. Calculate trigonometrical ratios of associated angle. 2. Solve the problems using above.
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• Lecture 23 (Chapter : Trigonometrical ratios and associated angles.) Solve the problems related to the above.
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• Lecture 24 ( Chapter : Trigonometrical ratios of compound angles ) Define compound angles. Establish the following relation geometrically for acute angles. i) sin (A ± B) = sin A cos B ± cos A sin B.
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• Lecture 25 ( Chapter : Trigonometrical ratios of compound angles ) ii) cos (A ± B) = cosA cosB ± sinAsinB.Deduce formula for tan (A ± B), Cot (A ± B). 10.4 Apply the identities to work out the problems:
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• Lecture 26 ( Chapter : Trigonometrical ratios of compound angles ) 1) find the value of sin 750, tan 750. ii) show that sin75° + sin15° sin75° – sin15° = 3
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• Lecture 27 (Transformation of Formula) Express sum or difference of two sines and cosines as a product and vice-versa
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• Lecture 28 (Transformation of Formula) Solve problems of the followings types: i) show that, sin55° + cos55° = 2 cos10°
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• Lecture 29 (Transformation of Formula) ii) prove that, cos80° cos60° cos40° cos20° =1/16
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• Lecture 30 (Multiple Angle) State the identities for sin 2A, cos 2A and tan 2A. Deduce formula for sin 3A, cos 3A and tan 3A.
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• Lecture 31 (Multiple Angle) if tan α = 2 tan β, show that, tan (α + β) = 3 sin 2α 1 + 3 cos 2α & Solve the problems related to the above.
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• Lecture 32 (Sub-multiple angles) Find mathematically the identities for sin α , cos α and tan α in terms of α2 and α3 Solve the problems of the type : find the value of cos 3°, cos 6°, cos 9°, etc.
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• Lecture 33 (Sub-multiple angles) Solve the problems of the type : cos 18°, cos 36° etc & Solve the problems related to the above.
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• Certification
• Certification on Mathematics-1